Bedazzling: The Size of Your Diamond Could Reveal Changes in the Fundamental Constants and the Existence Dark Matter

In the math that describes how the world works, there are some extraordinary numbers. These numbers, called fundamental constants, seem to be embedded in the very nature of the universe. They pop up whether you’re working in inches or centimeters, studying what happened billions of years ago or what’s happening today. Your very existence depends on them.

Handy wallet card displaying the fundamental constants. Credit: NIST

“We know that the fundamental constants are very finely tuned such that the observed universe works the way it does. If the values of some of these constants would change by a few percents, life could not exist,” explains Lukáš Pašteka, a researcher at Comenius University in Slovakia.

In addition to being fundamental, the values are constant—they don’t change in time or space. Probably. Maybe. Well, we don’t actually know. In 1937, theoretical physicist Paul Dirac proposed that some physical constants may change slightly as the universe evolves. Other theories have predicted slight variations in the values over space and/or time as well. Some astronomical observations support this idea, but they haven’t been conclusive. If the fundamental constants do change over time, the changes are small. Really small. “Incredibly tiny,” in Pašteka’s words. Smaller than 1 part in 100 quadrillion (1017) per year.

As reported in the American Physical Society’s journal Physical Review Letters, Pašteka and an international team of researchers recently proposed a new way to look for direct evidence of variations in two fundamental constants. In addition, their method could double as a new kind of dark matter detector, since dark matter is expected to cause variations of a different kind in the fundamental constants.

In order to be sensitive to such tiny changes, you need to make very precise measurements. This need laid the foundation for the new method. “The initial [research] idea was very simple,” says Pašteka. “We want to measure incredibly tiny changes in the values of fundamental constants, so why don’t we use the most precise measuring devices available to us, laser interferometers?”

Diagram of a laser interferometer. Credit: LIGO

If you’re a fan of gravitational waves, you’re probably familiar with laser interferometers. LIGO, the observatory that detected gravitational waves for the first time in 2015, measures tiny changes in length using laser interferometers. According to the LIGO team, the observatory can detect a change in length equal to 1/10,000th the width of a proton. “This is equivalent to measuring the distance to the nearest star (some 4.2 light years) to an accuracy smaller than the width of a human hair,” according to the LIGO website].

In simplified terms, laser interferometers such as LIGO’s works like this:. A laser beam is split so that light travels down two perpendicular paths. At the end of each path, the beam is reflected back. The two beams recombine and travel through a detector.  LIGO is set up so that the two recombining beams should destructively interfere—effectively canceling each other out. If they don’t, the length traveled by one or both of the beams has changed, and the size of this change can be determined from the interference pattern.

So how do you use a laser interferometer to measure a change in one of the fundamental constants? Answering that question took some thought. “We knew what we wanted to measure and what we wanted to measure it with, we just needed to connect the dots,” says Pašteka. Interferometers are all about measuring length, so the team eventually converged on the idea of looking for characteristic changes in the size of materials—solid objects—that would be caused by variations in either or both of two fundamental constants:

Zoom way in on a solid material, like a diamond, and you’ll see that it is made of atoms arranged in a rigid, repeating pattern. In fact, you can describe a solid by the lengths and angles between an atom and its neighbors. According to relativity, the spacing between atoms is partly determined by the fundamental constants α and µ. So, the researchers wondered, if α and/or µ were to change ever so slightly, how much would the length between atoms change? Enough that it could be measured with a laser interferometer?

Laser interference can reveal tiny changes in the atom spacings in a crystal. Image credit: L. F. Pašteka, Comenius University.

The answer wasn’t clear. No one had systematically studied how material size depends on the fundamental constants before, so the researchers decided to find out. They chose a range of materials including copper, gold, diamond, sapphire, tungsten carbide, and 11 others. Then, using a computer model, they calculated how the spacing between the atoms (or molecules) in each material would change with variations in α and with variations in µ.

These are not straightforward problems. “Our computational analysis took a bit over a year to finish, we wanted to be very careful and take into account all relevant contributions from different physical phenomena, however small they might be. We needed to be sure that we could use this method for the measuring of the tiny variation of fundamental constants,” says Pašteka.

The answers aren’t straightforward either. The results show that the α dependence of a material follows a discernable pattern, but the µ dependence doesn’t—it has to be calculated independently for each new material. But overall, the results are encouraging. The sensitivities are within the range of what could be detected by existing interferometers (with a few modifications) if α and/or µ change at the rate some suggest and data is collected over the course of a few years.

Laser interferometry isn’t the only possible technique for measuring these tiny changes and the researchers highlight a few other possibilities in their paper. However, all of ways involve precisely measuring the length of a solid over time, looking for incredibly tiny changes that would have big implications on our understanding of the universe.

Caliper measuring diamonds 

So, how would the size of a diamond change if the fundamental constants of the universe vary as some researchers propose? According to Pašteka, a diamond would shrink in length by a factor of roughly 0.00000000000000000001 (10-21) per year if α is changing. You’d need something waaaaaay more precise than a jeweler’s calipers to measure that change!

Kendra Redmond

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